Research on Gas Emission Prediction Based on KPCA-ICSA-SVR

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} div.type-section h2 { font-size: 20px; line-height: 26px; font-weight: 300; } div.type-section h3 { margin-left: 15px; margin-bottom: 0px; font-weight: 300; } .journal-tabs .tab-title.active a { } </style> <link rel="stylesheet" href="https://pub.mdpi-res.com/assets/css/slick.css?f38b2db10e01b157?1739885660"> <meta name="title" content="Research on Gas Emission Prediction Based on KPCA-ICSA-SVR"> <meta name="description" content="In the context of deep mining, the uncertainty of gas emission levels presents significant safety challenges for mines. This study proposes a gas emission prediction model based on Kernel Principal Component Analysis (KPCA), an Improved Crow Search Algorithm (ICSA) incorporating adaptive neighborhood search, and Support Vector Regression (SVR). Initially, data preprocessing is conducted to ensure a clean and complete dataset. Subsequently, KPCA is applied to reduce dimensionality by extracting key nonlinear features from the gas emission influencing factors, thereby enhancing computational efficiency. The ICSA is then employed to optimize SVR hyperparameters, improving the model’s optimization capabilities and generalization performance, leading to the development of a robust KPCA-ICSA-SVR prediction model. The results indicate that the KPCA-ICSA-SVR model achieves the best performance, with RMSE values of 0.17898 and 0.3071 for the training and testing sets, respectively, demonstrating superior robustness and generalization capability." > <link rel="image_src" href="https://pub.mdpi-res.com/img/journals/processes-logo.png?8600e93ff98dbf14" > <meta name="dc.title" content="Research on Gas Emission Prediction Based on KPCA-ICSA-SVR"> <meta name="dc.creator" content="Li Liu"> <meta name="dc.creator" content="Linchao Dai"> <meta name="dc.creator" content="Xinyi Mao"> <meta name="dc.creator" content="Yutao Chen"> <meta name="dc.creator" content="Yongheng Jing"> <meta name="dc.type" content="Article"> <meta name="dc.source" content="Processes 2024, Vol. 12, Page 2655"> <meta name="dc.date" content="2024-11-25"> <meta name ="dc.identifier" content="10.3390/pr12122655"> <meta name="dc.publisher" content="Multidisciplinary Digital Publishing Institute"> <meta name="dc.rights" content="http://creativecommons.org/licenses/by/3.0/"> <meta name="dc.format" content="application/pdf" > <meta name="dc.language" content="en" > <meta name="dc.description" content="In the context of deep mining, the uncertainty of gas emission levels presents significant safety challenges for mines. This study proposes a gas emission prediction model based on Kernel Principal Component Analysis (KPCA), an Improved Crow Search Algorithm (ICSA) incorporating adaptive neighborhood search, and Support Vector Regression (SVR). Initially, data preprocessing is conducted to ensure a clean and complete dataset. Subsequently, KPCA is applied to reduce dimensionality by extracting key nonlinear features from the gas emission influencing factors, thereby enhancing computational efficiency. The ICSA is then employed to optimize SVR hyperparameters, improving the model’s optimization capabilities and generalization performance, leading to the development of a robust KPCA-ICSA-SVR prediction model. The results indicate that the KPCA-ICSA-SVR model achieves the best performance, with RMSE values of 0.17898 and 0.3071 for the training and testing sets, respectively, demonstrating superior robustness and generalization capability." > <meta name="dc.subject" content="gas emission prediction" > <meta name="dc.subject" content="data preprocessing" > <meta name="dc.subject" content="prediction metrics" > <meta name="dc.subject" content="crow search optimization algorithm" > <meta name ="prism.issn" content="2227-9717"> <meta name ="prism.publicationName" content="Processes"> <meta name ="prism.publicationDate" content="2024-11-25"> <meta name ="prism.volume" content="12"> <meta name ="prism.number" content="12"> <meta name ="prism.section" content="Article" > <meta name ="prism.startingPage" content="2655" > <meta name="citation_issn" content="2227-9717"> <meta name="citation_journal_title" content="Processes"> <meta name="citation_publisher" content="Multidisciplinary Digital Publishing Institute"> <meta name="citation_title" content="Research on Gas Emission Prediction Based on KPCA-ICSA-SVR"> <meta name="citation_publication_date" content="2024/12"> <meta name="citation_online_date" content="2024/11/25"> <meta name="citation_volume" content="12"> <meta name="citation_issue" content="12"> <meta name="citation_firstpage" content="2655"> <meta name="citation_author" content="Liu, Li"> <meta name="citation_author" content="Dai, Linchao"> <meta name="citation_author" content="Mao, Xinyi"> <meta name="citation_author" content="Chen, Yutao"> <meta name="citation_author" content="Jing, Yongheng"> <meta name="citation_doi" content="10.3390/pr12122655"> <meta name="citation_id" content="mdpi-pr12122655"> <meta name="citation_abstract_html_url" content="https://www.mdpi.com/2227-9717/12/12/2655"> <meta name="citation_pdf_url" content="https://www.mdpi.com/2227-9717/12/12/2655/pdf?version=1732525120"> <link rel="alternate" type="application/pdf" title="PDF Full-Text" href="https://www.mdpi.com/2227-9717/12/12/2655/pdf?version=1732525120"> <meta name="fulltext_pdf" content="https://www.mdpi.com/2227-9717/12/12/2655/pdf?version=1732525120"> <meta name="citation_fulltext_html_url" content="https://www.mdpi.com/2227-9717/12/12/2655/htm"> <link rel="alternate" type="text/html" title="HTML Full-Text" href="https://www.mdpi.com/2227-9717/12/12/2655/htm"> <meta name="fulltext_html" content="https://www.mdpi.com/2227-9717/12/12/2655/htm"> <link rel="alternate" type="text/xml" title="XML Full-Text" href="https://www.mdpi.com/2227-9717/12/12/2655/xml"> <meta name="fulltext_xml" content="https://www.mdpi.com/2227-9717/12/12/2655/xml"> <meta name="citation_xml_url" content="https://www.mdpi.com/2227-9717/12/12/2655/xml"> <meta name="twitter:card" content="summary" /> <meta name="twitter:site" content="@MDPIOpenAccess" /> <meta name="twitter:image" content="https://pub.mdpi-res.com/img/journals/processes-logo-social.png?8600e93ff98dbf14" /> <meta property="fb:app_id" content="131189377574"/> <meta property="og:site_name" content="MDPI"/> <meta property="og:type" content="article"/> <meta property="og:url" content="https://www.mdpi.com/2227-9717/12/12/2655" /> <meta property="og:title" content="Research on Gas Emission Prediction Based on KPCA-ICSA-SVR" /> <meta property="og:description" content="In the context of deep mining, the uncertainty of gas emission levels presents significant safety challenges for mines. This study proposes a gas emission prediction model based on Kernel Principal Component Analysis (KPCA), an Improved Crow Search Algorithm (ICSA) incorporating adaptive neighborhood search, and Support Vector Regression (SVR). Initially, data preprocessing is conducted to ensure a clean and complete dataset. Subsequently, KPCA is applied to reduce dimensionality by extracting key nonlinear features from the gas emission influencing factors, thereby enhancing computational efficiency. The ICSA is then employed to optimize SVR hyperparameters, improving the model’s optimization capabilities and generalization performance, leading to the development of a robust KPCA-ICSA-SVR prediction model. The results indicate that the KPCA-ICSA-SVR model achieves the best performance, with RMSE values of 0.17898 and 0.3071 for the training and testing sets, respectively, demonstrating superior robustness and generalization capability." /> <meta property="og:image" content="https://pub.mdpi-res.com/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g001-550.jpg?1732525224" /> <link rel="alternate" type="application/rss+xml" title="MDPI Publishing - Latest articles" href="https://www.mdpi.com/rss"> <meta name="google-site-verification" content="PxTlsg7z2S00aHroktQd57fxygEjMiNHydKn3txhvwY"> <meta name="facebook-domain-verification" content="mcoq8dtq6sb2hf7z29j8w515jjoof7" /> <script id="Cookiebot" data-cfasync="false" src="https://consent.cookiebot.com/uc.js" data-cbid="51491ddd-fe7a-4425-ab39-69c78c55829f" type="text/javascript" async></script>  <script type="text/plain" data-cookieconsent="statistics"> (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); 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itemprop="name"> Research on Gas Emission Prediction Based on KPCA-ICSA-SVR </h1> <div class="art-authors hypothesis_container"> by <span class="inlineblock "><div class='profile-card-drop' data-dropdown='profile-card-drop13441932' data-options='is_hover:true, hover_timeout:5000'> Li Liu</div><div id="profile-card-drop13441932" data-dropdown-content class="f-dropdown content profile-card-content" aria-hidden="true" tabindex="-1"><div class="profile-card__title"><div class="sciprofiles-link" style="display: inline-block"><div class="sciprofiles-link__link"><img class="sciprofiles-link__image" src="/bundles/mdpisciprofileslink/img/unknown-user.png" style="width: auto; height: 16px; border-radius: 50%;"><span class="sciprofiles-link__name">Li Liu</span></div></div></div><div class="profile-card__buttons" style="margin-bottom: 10px;"><a href="https://sciprofiles.com/profile/3964680?utm_source=mdpi.com&utm_medium=website&utm_campaign=avatar_name" class="button button--color-inversed" 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src="/bundles/mdpisciprofileslink/img/unknown-user.png" style="width: auto; height: 16px; border-radius: 50%;"><span class="sciprofiles-link__name">Yongheng Jing</span></div></div></div><div class="profile-card__buttons" style="margin-bottom: 10px;"><a href="https://sciprofiles.com/profile/4059660?utm_source=mdpi.com&utm_medium=website&utm_campaign=avatar_name" class="button button--color-inversed" target="_blank"> SciProfiles </a><a href="https://scilit.com/scholars?q=Yongheng%20Jing" class="button button--color-inversed" target="_blank"> Scilit </a><a href="https://www.preprints.org/search?search1=Yongheng%20Jing&field1=authors" class="button button--color-inversed" target="_blank"> Preprints.org </a><a href="https://scholar.google.com/scholar?q=Yongheng%20Jing" class="button button--color-inversed" target="_blank" rels="noopener noreferrer"> Google Scholar </a></div></div><sup> 1</sup><span style="display: inline; margin-left: 5px;"></span><a class="toEncode emailCaptcha visibility-hidden" data-author-id="13441936" href="/cdn-cgi/l/email-protection#3b1458555f16585c521457145e565a5257164b49544f5e584f525455180b0b0a080d5a0b09095a0a020a5e0a5d0f0f0a090a5d0a020a5e0f0f0b5d0b5e0a5d0f0f0b020b0f"><sup><i class="fa fa-envelope-o"></i></sup></a></span> </div> <div class="nrm"></div> <span style="display:block; height:6px;"></span> <div></div> <div style="margin: 5px 0 15px 0;" class="hypothesis_container"> <div class="art-affiliations"> <div class="affiliation "> <div class="affiliation-item"><sup>1</sup></div> <div class="affiliation-name ">College of Safety Science and Engineering, Xi’an University of Science and Technology, Xi’an 710054, China</div> </div> <div class="affiliation "> <div class="affiliation-item"><sup>2</sup></div> <div class="affiliation-name ">State Key Laboratory of Coal Mine Disaster Prevention and Control, Chongqing 400037, China</div> </div> <div class="affiliation "> <div class="affiliation-item"><sup>3</sup></div> <div class="affiliation-name ">China Coal Technology and Engineering Group, Chongqing Research Institute, Chongqing 400037, China</div> </div> <div class="affiliation"> <div class="affiliation-item"><sup>*</sup></div> <div class="affiliation-name ">Authors to whom correspondence should be addressed. </div> </div> </div> </div> <div class="bib-identity" style="margin-bottom: 10px;"> <em>Processes</em> <b>2024</b>, <em>12</em>(12), 2655; <a href="https://doi.org/10.3390/pr12122655">https://doi.org/10.3390/pr12122655</a> </div> <div class="pubhistory" style="font-weight: bold; padding-bottom: 10px;"> <span style="display: inline-block">Submission received: 6 November 2024</span> / <span style="display: inline-block">Revised: 20 November 2024</span> / <span style="display: inline-block">Accepted: 22 November 2024</span> / <span style="display: inline-block">Published: 25 November 2024</span> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/processes/special_issues/01A0J40BNO ">Advances in Coal Processing, Utilization, and Process Safety</a>)<br/> </div> <div class="highlight-box1"> <div class="download"> <a class="button button--color-inversed button--drop-down" data-dropdown="drop-download-1528631" aria-controls="drop-supplementary-1528631" aria-expanded="false"> Download <i class="material-icons">keyboard_arrow_down</i> </a> <div id="drop-download-1528631" class="f-dropdown label__btn__dropdown label__btn__dropdown--button" data-dropdown-content aria-hidden="true" tabindex="-1"> <a class="UD_ArticlePDF" href="/2227-9717/12/12/2655/pdf?version=1732525120" data-name="Research on Gas Emission Prediction Based on KPCA-ICSA-SVR" data-journal="processes">Download PDF</a> <br/> <a id="js-pdf-with-cover-access-captcha" href="#" data-target="/2227-9717/12/12/2655/pdf-with-cover" class="accessCaptcha">Download PDF with Cover</a> <br/> <a id="js-xml-access-captcha" href="#" 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href="https://pub.mdpi-res.com/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g003.png?1732525225" title=" <strong>Figure 3</strong><br/> <p>Schematic diagram of SVR.</p> "> </a> <a href="https://pub.mdpi-res.com/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g004.png?1732525225" title=" <strong>Figure 4</strong><br/> <p>RMSE of different estimators.</p> "> </a> <a href="https://pub.mdpi-res.com/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g005.png?1732525226" title=" <strong>Figure 5</strong><br/> <p>Kernel matrix heatmap.</p> "> </a> <a href="https://pub.mdpi-res.com/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g006.png?1732525227" title=" <strong>Figure 6</strong><br/> <p>Variance explanation.</p> "> </a> <a href="https://pub.mdpi-res.com/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g007.png?1732525229" title=" <strong>Figure 7</strong><br/> <p>Optimization capabilities of the algorithm: (<b>a</b>) unimodal function; (<b>b</b>) multimodal function.</p> "> </a> <a href="https://pub.mdpi-res.com/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g008.png?1732525231" title=" <strong>Figure 8</strong><br/> <p>Training set prediction results.</p> "> </a> <a href="https://pub.mdpi-res.com/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g009.png?1732525231" title=" <strong>Figure 9</strong><br/> <p>Test set prediction results</p> "> </a> </div> <a class="button button--color-inversed" href="/2227-9717/12/12/2655/notes">Versions Notes</a> </div> </div> <div class="responsive-moving-container small hidden" data-id="article-counters" style="margin-top: 15px;"></div> <div class="html-dynamic"> <section> <div class="art-abstract art-abstract-new in-tab hypothesis_container"> <p> <div><section class="html-abstract" id="html-abstract"> <h2 id="html-abstract-title">Abstract</h2><b>:</b> <div class="html-p">In the context of deep mining, the uncertainty of gas emission levels presents significant safety challenges for mines. This study proposes a gas emission prediction model based on Kernel Principal Component Analysis (KPCA), an Improved Crow Search Algorithm (ICSA) incorporating adaptive neighborhood search, and Support Vector Regression (SVR). Initially, data preprocessing is conducted to ensure a clean and complete dataset. Subsequently, KPCA is applied to reduce dimensionality by extracting key nonlinear features from the gas emission influencing factors, thereby enhancing computational efficiency. The ICSA is then employed to optimize SVR hyperparameters, improving the model’s optimization capabilities and generalization performance, leading to the development of a robust KPCA-ICSA-SVR prediction model. The results indicate that the KPCA-ICSA-SVR model achieves the best performance, with RMSE values of 0.17898 and 0.3071 for the training and testing sets, respectively, demonstrating superior robustness and generalization capability.</div> </section> <div id="html-keywords"> <div class="html-gwd-group"><div id="html-keywords-title">Keywords: </div><a href="/search?q=gas+emission+prediction">gas emission prediction</a>; <a href="/search?q=data+preprocessing">data preprocessing</a>; <a href="/search?q=prediction+metrics">prediction metrics</a>; <a href="/search?q=crow+search+optimization+algorithm">crow search optimization algorithm</a></div> <div> </div> </div> </div> </p> </div> </section> </div> <div class="hypothesis_container"> <ul class="menu html-nav" data-prev-node="#html-quick-links-title"> </ul> <div class="html-body"> <section id='sec1-processes-12-02655' type='intro'><h2 data-nested='1'> 1. Introduction</h2><div class='html-p'>Coal continues to play a pivotal role in China’s energy consumption, acting as a primary energy source in critical sectors such as electricity generation, industry, and transportation, owing to its abundant reserves and relatively low cost [<a href="#B1-processes-12-02655" class="html-bibr">1</a>,<a href="#B2-processes-12-02655" class="html-bibr">2</a>,<a href="#B3-processes-12-02655" class="html-bibr">3</a>]. However, as mining depth increases, the complexity of gas emissions also rises, posing significant safety risks in underground operations. Gas emissions not only deteriorate the mine environment and disrupt equipment function, but they also elevate underground gas concentrations, substantially increasing the risk of gas explosions and presenting a direct threat to the continuity of mining activities and miner safety. The variability and unpredictability of gas emissions, influenced by factors such as geological structures, coal seam characteristics, and mining methods, render traditional prediction approaches insufficiently responsive. Therefore, accurately forecasting gas emissions is crucial for ensuring mine safety and mitigating the occurrence of hazardous incidents [<a href="#B4-processes-12-02655" class="html-bibr">4</a>,<a href="#B5-processes-12-02655" class="html-bibr">5</a>,<a href="#B6-processes-12-02655" class="html-bibr">6</a>,<a href="#B7-processes-12-02655" class="html-bibr">7</a>,<a href="#B8-processes-12-02655" class="html-bibr">8</a>].</div><div class='html-p'>Extensive research has been conducted both domestically and internationally on methods for predicting gas emissions in mining. Guo et al. [<a href="#B9-processes-12-02655" class="html-bibr">9</a>] designed a gas emission prediction system using wavelet denoising combined with BP neural networks and validated its accuracy experimentally. Zhang et al. [<a href="#B10-processes-12-02655" class="html-bibr">10</a>] applied the Bootstrap sampling method, using out-of-bag (OOB) data scores (oob_score) to tune the model and assess feature importance, ultimately determining the optimal parameters and feature variable importance proportions for constructing their predictive model. Yan et al. [<a href="#B11-processes-12-02655" class="html-bibr">11</a>] utilized factor analysis to extract prediction indicators and developed a gas emission prediction model using a particle swarm-optimized radial basis function (RBF) neural network. However, BP neural networks are prone to noise and outliers, with training processes that can become trapped in local optima; random forest (RF) models lack interpretability, making it challenging to analyze the specific contribution of each feature to the prediction results; and RBF models face issues like the “curse of dimensionality” when handling high-dimensional data, potentially leading to decreased model performance. Furthermore, these models tend to have limited generalization abilities, low robustness to small sample sizes, and difficulties in capturing complex nonlinear relationships, thereby constraining their precision in gas emission prediction [<a href="#B12-processes-12-02655" class="html-bibr">12</a>,<a href="#B13-processes-12-02655" class="html-bibr">13</a>,<a href="#B14-processes-12-02655" class="html-bibr">14</a>].</div><div class='html-p'>In this study, we address the complexity and multifactorial nature of gas emission prediction. Initially, data were preprocessed through cleaning and normalization, followed by the establishment of a comprehensive index system for gas emission prediction. To enhance predictive accuracy, Kernel Principal Component Analysis (KPCA) was introduced to perform feature extraction and dimensionality reduction, preserving critical information while reducing dimensional complexity, which improves model learning efficiency. Furthermore, an adaptive neighborhood search combined with reinforcement learning optimizes the Crow Search Algorithm (CSA) to fine-tune the SVR model’s hyperparameters, enhancing convergence speed and global search capability. The resulting KPCA-ICSA-SVR model effectively captures the nonlinear characteristics of gas emissions, yielding more accurate and reliable predictions [<a href="#B15-processes-12-02655" class="html-bibr">15</a>].</div></section><section id='sec2-processes-12-02655' type=''><h2 data-nested='1'> 2. Formulation of Foundational Principles for Processes and Algorithms</h2><section id='sec2dot1-processes-12-02655' type=''><h4 class='html-italic' data-nested='2'> 2.1. Process for Establishing Predictive Models</h4><div class='html-p'>The specific process for establishing a coal and gas outburst prediction model is as follows:</div><div class='html-p'>(1) Data Collection and Preprocessing: Gas emission data are collected and undergo comprehensive preprocessing. Outliers within the dataset are identified and removed using Boxplot analysis, thereby minimizing the impact of extreme values on model accuracy. Missing values are addressed through multiple imputation (MI), improving the completeness and quality of the data. Normalization is applied to remove scaling effects between features. Subsequently, Kernel Principal Component Analysis (KPCA) is employed for feature extraction and dimensionality reduction on the preprocessed data, retaining essential variable information while reducing dimensionality to optimize computational efficiency.</div><div class='html-p'>(2) Algorithm Optimization with Improved Crow Search (ICSA): An Improved Crow Search Algorithm (ICSA) is developed by integrating adaptive neighborhood search and reinforcement learning strategies. The adaptive neighborhood search adjusts search scopes dynamically, enhancing the algorithm’s flexibility, while the reinforcement learning strategy accumulates experience to improve optimization efficiency and accuracy throughout the process. The ICSA’s robust global and local search capabilities enable efficient exploration of the parameter space, fine-tuning the SVR model’s hyperparameters, and yielding an optimal parameter set for gas emission prediction.</div><div class='html-p'>(3) Model Construction and Comparative Evaluation: After data preprocessing and hyperparameter optimization, comparative models are established to evaluate prediction effectiveness. Benchmark models such as BP, KPCA-ICSA-BP, and SVR are constructed. Evaluation metrics, including RMSE and MPE, are used to assess the performance of each model in gas emission prediction. Results indicate that the KPCA-ICSA-SVR model demonstrates a substantial advantage in prediction accuracy and generalization capability, capturing the nonlinear characteristics of gas emissions more effectively.</div></section><section id='sec2dot2-processes-12-02655' type=''><h4 class='html-italic' data-nested='2'> 2.2. Basic Principles of the Algorithm</h4><section id='sec2dot2dot1-processes-12-02655' type=''><h4 class='' data-nested='3'> 2.2.1. Kernel Principal Component Analysis, KPCA</h4><div class='html-p'>Principal Component Analysis (PCA) is a classical dimensionality reduction technique that projects data into a lower-dimensional space via linear transformations, aiming to preserve as much of the original data’s variance as possible. PCA is widely used in data preprocessing, feature extraction, and pattern recognition. However, the linear assumptions of PCA limit its effectiveness in handling complex, high-dimensional nonlinear data. In many real-world applications, data often exhibit significant nonlinearity, which constrains PCA’s capacity to fully capture the inherent patterns and relationships within the data [<a href="#B16-processes-12-02655" class="html-bibr">16</a>,<a href="#B17-processes-12-02655" class="html-bibr">17</a>].</div><div class='html-p'>To address this limitation, KPCA was developed [<a href="#B18-processes-12-02655" class="html-bibr">18</a>,<a href="#B19-processes-12-02655" class="html-bibr">19</a>]. By incorporating kernel techniques, KPCA maps data into a high-dimensional feature space where nonlinear features can be more effectively captured using kernel functions such as the Gaussian or polynomial kernel. This approach enables principal component analysis in this new feature space, retaining the dimensionality reduction advantages of PCA while significantly enhancing its ability to model nonlinear structures. KPCA has demonstrated superior performance in fields like pattern recognition and data mining, effectively improving both the accuracy and robustness of data analysis (<a href="#processes-12-02655-f001" class="html-fig">Figure 1</a>).</div><div class='html-p'>(1) Data Standardization: The initial step in KPCA involves standardizing the original dataset X = {x<sub>1</sub>,x<sub>2</sub>,…,x<span class='html-italic'><sub>n</sub></span>} to ensure that all features are on a similar scale. For each sample, x<span class='html-italic'><sub>i</sub></span>∈R<span class='html-italic'><sup>m</sup></span>. The standardization formula is as follows (1):<div class='html-disp-formula-info' id='FD1-processes-12-02655'> <div class='f'> <math display='block'><semantics> <mrow> <msubsup> <mi mathvariant="normal">x</mi> <mi>i</mi> <mo>′</mo> </msubsup> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <msub> <mi mathvariant="normal">x</mi> <mi>i</mi> </msub> <mo>−</mo> <mi>μ</mi> </mrow> <mi>σ</mi> </mfrac> </mstyle> </mrow> </semantics></math> </div> <div class='l'> <label >(1)</label> </div> </div> where <span class='html-italic'>µ</span> is the mean and <span class='html-italic'>σ</span> is the standard deviation.</div><div class='html-p'>(2) Select Kernel Function: Choose an appropriate kernel function <span class='html-italic'>K</span>. In this study, the Gaussian kernel is selected, with the calculation formula given by the following (2):<div class='html-disp-formula-info' id='FD2-processes-12-02655'> <div class='f'> <math display='block'><semantics> <mrow> <mi>K</mi> <mfenced> <mrow> <msub> <mi mathvariant="normal">x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi mathvariant="normal">x</mi> <mi>j</mi> </msub> </mrow> </mfenced> <mo>=</mo> <mi>exp</mi> <mfenced> <mrow> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <msup> <mrow> <mfenced close="‖" open="‖"> <mrow> <msub> <mi mathvariant="normal">x</mi> <mi>i</mi> </msub> <mo>−</mo> <msub> <mi mathvariant="normal">x</mi> <mi>j</mi> </msub> </mrow> </mfenced> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <msup> <mi>σ</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mstyle> </mrow> </mfenced> </mrow> </semantics></math> </div> <div class='l'> <label >(2)</label> </div> </div></div><div class='html-p'>(3) Construct Kernel Matrix: Calculate the kernel matrix K, where the elements are given by <span class='html-italic'>K<sub>ij</sub> </span>= <span class='html-italic'>K</span>(x<span class='html-italic'><sub>i</sub></span>,x<span class='html-italic'><sub>j</sub></span>). The dimension of the kernel matrix is <span class='html-italic'>n</span> × <span class='html-italic'>n</span>, where <span class='html-italic'>n</span> is the number of samples.</div><div class='html-p'>(4) Center the Kernel Matrix: Perform centering on the kernel matrix to eliminate the influence of the mean. The centering formula is given by the following (3):<div class='html-disp-formula-info' id='FD3-processes-12-02655'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi mathvariant="normal">K</mi> <mrow> <mi>centered</mi> </mrow> </msub> <mo>=</mo> <mi mathvariant="normal">K</mi> <mo>−</mo> <msub> <mn>1</mn> <mi>n</mi> </msub> <mi mathvariant="normal">K</mi> <mo>−</mo> <mi mathvariant="normal">K</mi> <msub> <mn>1</mn> <mi>n</mi> </msub> <mo>+</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mstyle> <msub> <mn>1</mn> <mi>n</mi> </msub> <mi mathvariant="normal">K</mi> <msub> <mn>1</mn> <mi>n</mi> </msub> </mrow> </semantics></math> </div> <div class='l'> <label >(3)</label> </div> </div> where 1<span class='html-italic'><sub>n</sub></span> is an <span class='html-italic'>n</span> × <span class='html-italic'>n</span> matrix of ones.</div><div class='html-p'>(5) Compute Eigenvalues and Eigenvectors: Perform eigenvalue decomposition on the centered kernel matrix K<sub>centered</sub> to obtain the eigenvalues <span class='html-italic'>λ<sub>i</sub></span> and the corresponding eigenvectors <span class='html-italic'>v<sub>i</sub></span> (4):<div class='html-disp-formula-info' id='FD4-processes-12-02655'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi mathvariant="normal">K</mi> <mrow> <mi>centered</mi> </mrow> </msub> <msub> <mi mathvariant="normal">v</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>λ</mi> <mi>i</mi> </msub> <msub> <mi mathvariant="normal">v</mi> <mi>i</mi> </msub> </mrow> </semantics></math> </div> <div class='l'> <label >(4)</label> </div> </div></div><div class='html-p'>(6) Select Principal Components: Choose the top <span class='html-italic'>d</span> eigenvectors in descending order of eigenvalues to form the feature matrix V<span class='html-italic'><sub>d</sub></span> = [v<sub>1</sub>,v<sub>2</sub>,…,v<span class='html-italic'><sub>d</sub></span>].</div><div class='html-p'>(7) Dimensionality Reduction Mapping: Map the original data into a lower-dimensional feature space to obtain the reduced data Y (5):<div class='html-disp-formula-info' id='FD5-processes-12-02655'> <div class='f'> <math display='block'><semantics> <mrow> <mi mathvariant="normal">Y</mi> <mo>=</mo> <msub> <mi mathvariant="normal">K</mi> <mrow> <mi>centered</mi> </mrow> </msub> <msub> <mi mathvariant="normal">V</mi> <mi>d</mi> </msub> </mrow> </semantics></math> </div> <div class='l'> <label >(5)</label> </div> </div> Typically, the reduced representation of each sample is expressed as follows (6):<div class='html-disp-formula-info' id='FD6-processes-12-02655'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>=</mo> <mstyle displaystyle="true"> <munderover> <mo>∑</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mi>K</mi> <mfenced> <mrow> <msub> <mi mathvariant="normal">x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi mathvariant="normal">x</mi> <mi>j</mi> </msub> </mrow> </mfenced> </mrow> </mstyle> <msub> <mi>α</mi> <mi>j</mi> </msub> </mrow> </semantics></math> </div> <div class='l'> <label >(6)</label> </div> </div> where <span class='html-italic'>α<sub>j</sub></span> is the coefficient of the corresponding eigenvector.</div><div class='html-p'>(8) Result Output: Output the reduced data Y, where each column represents a principal component.</div></section><section id='sec2dot2dot2-processes-12-02655' type=''><h4 class='' data-nested='3'> 2.2.2. Improved Crow Search Algorithm, ICSA</h4><div class='html-p'>The Crow Search Algorithm (CSA) is a population-based intelligent optimization algorithm inspired by the foraging behavior of crows [<a href="#B20-processes-12-02655" class="html-bibr">20</a>,<a href="#B21-processes-12-02655" class="html-bibr">21</a>,<a href="#B22-processes-12-02655" class="html-bibr">22</a>]. By simulating the memory and defense strategies of crows, the CSA searches for optimal solutions within the solution space. It is characterized by its simplicity and wide applicability, having demonstrated effective results across various optimization problems. However, the CSA tends to get trapped in local optima during the search process, and its balance between exploration and exploitation is limited, leading to slower convergence speeds and insufficient precision in complex, multi-modal, high-dimensional problems [<a href="#B23-processes-12-02655" class="html-bibr">23</a>].</div><div class='html-p'>To address these limitations, this study proposes an Improved Crow Search Algorithm (ICSA), which integrates adaptive neighborhood search and reinforcement learning strategies. First, adaptive neighborhood search dynamically adjusts the search radius of crows, ensuring flexibility in exploration during different search phases; this allows for extensive searching in the early stages while gradually focusing on fine-tuning in later stages. Furthermore, the incorporation of reinforcement learning allows the crows to adaptively select optimal search behaviors based on feedback from the environment, thereby enhancing the algorithm’s decision-making capabilities. This improvement not only strengthens the CSA’s global exploration capabilities and local search accuracy but also significantly increases convergence speed and solution precision, resulting in enhanced robustness and stability in tackling complex optimization problems. A schematic representation of the ICSA is shown in <a href="#processes-12-02655-f002" class="html-fig">Figure 2</a>.</div><div class='html-p'>The detailed steps and key formulas for the Improved Crow Search Algorithm (ICSA) are as follows:</div><div class='html-p'>(1) Initialize Population: Initialize the position x<span class='html-italic'><sub>i</sub></span> and memory position m<span class='html-italic'><sub>i</sub></span> of each crow in the population, along with their respective fitness values. Set the adaptive neighborhood radius <span class='html-italic'>δ<sub>i</sub></span> and learning rate <span class='html-italic'>α<sub>i</sub></span>, as well as the Q-table for reinforcement learning, which will be used to learn the optimal behaviors for different states.</div><div class='html-p'>(2) Adaptive Neighborhood Search: Establish the neighborhood radius <span class='html-italic'>δ<sub>i</sub></span> and dynamically adjust the search neighborhood. Define the initial radius <span class='html-italic'>δ<sub>init</sub></span> and a scaling factor <span class='html-italic'>γ</span> (where <span class='html-italic'>γ</span> ∈ (0, 1)). Adjust the neighborhood radius based on the current population density and fitness, allowing the search range to adaptively change during the optimization process (7):<div class='html-disp-formula-info' id='FD7-processes-12-02655'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>δ</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>δ</mi> <mrow> <mi>init</mi> </mrow> </msub> <mo>×</mo> <msup> <mi>γ</mi> <mrow> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mn>1</mn> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mstyle> </mrow> </msup> </mrow> </semantics></math> </div> <div class='l'> <label >(7)</label> </div> </div> where <span class='html-italic'>t</span> is the current iteration, and <span class='html-italic'>γ</span> controls the contraction rate.</div><div class='html-p'>(3) Reinforcement Learning Strategy: Apply Q-learning in reinforcement learning to establish a behavior selection strategy. Define the state <span class='html-italic'>S</span> (including information like current position and fitness) and the actions <span class='html-italic'>A</span> (choosing neighborhood search or extended search). Update each crow’s Q-value with the learning rate <span class='html-italic'>η</span> and discount factor <span class='html-italic'>λ</span>. The Q-value update formula is as follows (8):<div class='html-disp-formula-info' id='FD8-processes-12-02655'> <div class='f'> <math display='block'><semantics> <mrow> <mi>Q</mi> <mfenced> <mrow> <mi>S</mi> <mo>,</mo> <mi>A</mi> </mrow> </mfenced> <mo>←</mo> <mi>Q</mi> <mfenced> <mrow> <mi>S</mi> <mo>,</mo> <mi>A</mi> </mrow> </mfenced> <mo>+</mo> <mi>η</mi> <mfenced close="]" open="["> <mrow> <mi>r</mi> <mo>+</mo> <mi>λ</mi> <mo>⋅</mo> <munder> <mrow> <mi>max</mi> </mrow> <mrow> <msup> <mi>A</mi> <mo>′</mo> </msup> </mrow> </munder> <mi>Q</mi> <mfenced> <mrow> <msup> <mi>S</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>A</mi> <mo>′</mo> </msup> </mrow> </mfenced> <mo>−</mo> <mi>Q</mi> <mfenced> <mrow> <mi>S</mi> <mo>,</mo> <mi>A</mi> </mrow> </mfenced> </mrow> </mfenced> </mrow> </semantics></math> </div> <div class='l'> <label >(8)</label> </div> </div> where <span class='html-italic'>r</span> is the reward obtained from the current action, and <span class='html-italic'>S’</span> is the new state resulting from action <span class='html-italic'>A</span>.</div><div class='html-p'>(4) Position Update: Based on neighborhood search and reinforcement learning decisions, choose whether to utilize the memory position (for local search) or perform global exploration (9):<div class='html-disp-formula-info' id='FD9-processes-12-02655'> <div class='f'> <math display='block'><semantics> <mrow> <msubsup> <mi mathvariant="normal">x</mi> <mi>i</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <mfenced close="" open="{"> <mrow> <mtable columnalign="left" equalrows="true" equalcolumns="true"> <mtr columnalign="left"> <mtd columnalign="left"> <mrow> <msubsup> <mi mathvariant="normal">x</mi> <mi>i</mi> <mi>t</mi> </msubsup> <mo>+</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>⋅</mo> <msub> <mi>δ</mi> <mi>i</mi> </msub> <mo>⋅</mo> <mo stretchy="false">(</mo> <msub> <mi mathvariant="normal">m</mi> <mi>j</mi> </msub> <mo>−</mo> <msubsup> <mi mathvariant="normal">x</mi> <mi>i</mi> <mi>t</mi> </msubsup> <mo stretchy="false">)</mo> <mo>,</mo> </mrow> </mtd> <mtd columnalign="left"> <mrow> <mrow> <mi>if</mi> <mo> </mo> <mi>global</mi> </mrow> </mrow> </mtd> </mtr> <mtr columnalign="left"> <mtd columnalign="left"> <mrow> <msubsup> <mi mathvariant="normal">x</mi> <mi>i</mi> <mi>t</mi> </msubsup> <mo>+</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>⋅</mo> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>⋅</mo> <mo stretchy="false">(</mo> <msub> <mi mathvariant="normal">m</mi> <mi>i</mi> </msub> <mo>−</mo> <msubsup> <mi mathvariant="normal">x</mi> <mi>i</mi> <mi>t</mi> </msubsup> <mo stretchy="false">)</mo> <mo>,</mo> </mrow> </mtd> <mtd columnalign="left"> <mrow> <mrow> <mi>if</mi> <mo> </mo> <mi>local</mi> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mfenced> </mrow> </semantics></math> </div> <div class='l'> <label >(9)</label> </div> </div> where <span class='html-italic'>r<sub>i</sub></span> is a random number in the range (0,1).</div><div class='html-p'>(5) Memory Position Update: If the new position X<sub>i</sub><span class='html-italic'><sup>t</sup></span><sup>+1</sup> is better than the memory position m<span class='html-italic'><sub>i</sub></span>, update m<span class='html-italic'><sub>i</sub></span> with X<sub>i</sub><span class='html-italic'><sup>t</sup></span><sup>+1</sup>.</div><div class='html-p'>(6) Adaptive Adjustment of Neighborhood Radius and Learning Rate: Based on the crow’s fitness and population diversity, adaptively adjust the neighborhood radius <span class='html-italic'>δ<sub>i</sub></span> and learning rate <span class='html-italic'>α<sub>i</sub></span> to ensure a larger exploration range in the early stages and more focused local searches later on (10):<div class='html-disp-formula-info' id='FD10-processes-12-02655'> <div class='f'> <math display='block'><semantics> <mtable columnalign="left"> <mtr> <mtd> <msub> <mi>δ</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>δ</mi> <mrow> <mi>init</mi> </mrow> </msub> <mo>×</mo> <mi>exp</mi> <mfenced> <mrow> <mo>−</mo> <mi>β</mi> <mo>⋅</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mi>t</mi> <mi>T</mi> </mfrac> </mstyle> </mrow> </mfenced> </mtd> </mtr> <mtr> <mtd> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>α</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>×</mo> <mi>exp</mi> <mfenced> <mrow> <mo>−</mo> <mi>γ</mi> <mo>⋅</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mi>t</mi> <mi>T</mi> </mfrac> </mstyle> </mrow> </mfenced> </mtd> </mtr> </mtable> </semantics></math> </div> <div class='l'> <label >(10)</label> </div> </div> where <span class='html-italic'>β</span> and <span class='html-italic'>γ</span> control the decay rates of the radius and learning rate, respectively, and <span class='html-italic'>T</span> is the maximum number of iterations.</div><div class='html-p'>(7) Stopping Criteria: The iteration process halts if a predefined maximum number of iterations is reached or if convergence criteria are met (e.g., the fitness value shows no significant improvement), and the optimal solution is outputted.</div></section><section id='sec2dot2dot3-processes-12-02655' type=''><h4 class='' data-nested='3'> 2.2.3. Support Vector Regression, SVR</h4><div class='html-p'>Support Vector Regression (SVR) is a regression model well suited for scenarios with small sample sizes and high-dimensional data [<a href="#B24-processes-12-02655" class="html-bibr">24</a>,<a href="#B25-processes-12-02655" class="html-bibr">25</a>,<a href="#B26-processes-12-02655" class="html-bibr">26</a>]. In gas emission prediction, where data collection is challenging and sample sizes are typically limited, traditional methods may struggle to achieve satisfactory accuracy under small sample conditions or in high-dimensional spaces. SVR constructs an optimal regression hyperplane in the feature space, minimizing prediction error while controlling it within an <span class='html-italic'>ϵ</span>-insensitive margin, providing strong generalization ability and robustness to small sample sizes. This approach effectively handles the nonlinearity and high-risk factors inherent in gas emission prediction, making it ideal for small-sample data analysis and significantly enhancing prediction accuracy and reliability. An SVR illustration is shown in <a href="#processes-12-02655-f003" class="html-fig">Figure 3</a>.</div><div class='html-p'>The detailed steps and key formulas for the SVR are as follows:</div><div class='html-p'>(1) Data Preparation: A training dataset is given by {(x<span class='html-italic'><sub>i</sub></span>,<span class='html-italic'>y<sub>i</sub></span>)}<span class='html-italic'><sup>n</sup><sub>i</sub></span><sub>=1</sub>, where x<span class='html-italic'><sub>i</sub></span>∈R<sup>m</sup> is the feature vector of the <span class='html-italic'>i</span>-th sample, and <span class='html-italic'>y<sub>i</sub></span>∈R is the corresponding continuous target value.</div><div class='html-p'>(2) Kernel Trick: Since the data may not be linearly separable, a kernel function is used to map the data into a higher-dimensional space, making them closer to linearly separable in the new space. In this study, the Gaussian kernel is chosen.</div><div class='html-p'>(3) ϵ-Insensitive Loss and Soft Margin SVR: The <span class='html-italic'>ϵ</span>-insensitive loss function is introduced, allowing the model to ignore errors within the ±<span class='html-italic'>ϵ</span> range. This enables the model to tolerate some error within the <span class='html-italic'>ϵ</span> margin without penalizing the optimization objective. Slack variables <span class='html-italic'>ξ<sub>i</sub> </span>≥ 0 and <span class='html-italic'>ξ<sub>i</sub><sup>*</sup> </span>≥ 0 are introduced to represent errors that exceed the <span class='html-italic'>ϵ</span> margin on the upper and lower sides, respectively. The objective is to minimize the complexity of the regression model while controlling the prediction error (11):<div class='html-disp-formula-info' id='FD11-processes-12-02655'> <div class='f'> <math display='block'><semantics> <mrow> <mi>min</mi> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> <msup> <mrow> <mfenced close="‖" open="‖"> <mi mathvariant="normal">w</mi> </mfenced> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mi>C</mi> <mstyle displaystyle="true"> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mfenced> <mrow> <msub> <mi>ξ</mi> <mi>i</mi> </msub> <mo>+</mo> <msubsup> <mi>ξ</mi> <mi>i</mi> <mo>*</mo> </msubsup> </mrow> </mfenced> </mrow> </mstyle> </mrow> </semantics></math> </div> <div class='l'> <label >(11)</label> </div> </div> where <span class='html-italic'>ξ<sub>i</sub></span> and <span class='html-italic'>ξ<sub>i</sub><sup>*</sup></span> represent the errors above the upper bound and below the lower bound, respectively. <span class='html-italic'>C</span> is a hyperparameter that balances the model complexity and the penalty for errors.</div><div class='html-p'>(4) Dual Problem: To incorporate the kernel function, the original optimization problem is transformed into its dual form. Lagrange multipliers <span class='html-italic'>α<sub>i</sub></span> and <span class='html-italic'>α<sub>i</sub><sup>*</sup></span> are introduced to represent the weights for each data point. The dual problem can be expressed as follows (12):<div class='html-disp-formula-info' id='FD12-processes-12-02655'> <div class='f'> <math display='block'><semantics> <mrow> <mi>max</mi> <mstyle displaystyle="true"> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mfenced> <mrow> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>−</mo> <msubsup> <mi>α</mi> <mi>i</mi> <mo>*</mo> </msubsup> </mrow> </mfenced> </mrow> </mstyle> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>−</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> <mstyle displaystyle="true"> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mstyle displaystyle="true"> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mfenced> <mrow> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>−</mo> <msubsup> <mi>α</mi> <mi>i</mi> <mo>*</mo> </msubsup> </mrow> </mfenced> <mfenced> <mrow> <msub> <mi>α</mi> <mi>j</mi> </msub> <mo>−</mo> <msubsup> <mi>α</mi> <mi>j</mi> <mo>*</mo> </msubsup> </mrow> </mfenced> </mrow> </mstyle> </mrow> </mstyle> <mi>K</mi> <mfenced> <mrow> <msub> <mi mathvariant="normal">x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi mathvariant="normal">x</mi> <mi>j</mi> </msub> </mrow> </mfenced> </mrow> </semantics></math> </div> <div class='l'> <label >(12)</label> </div> </div> subject to 0 ≤ <span class='html-italic'>α<sub>i</sub></span>, <span class='html-italic'>α<sub>i</sub><sup>*</sup> </span>≤ <span class='html-italic'>C</span> and <math display='inline'><semantics> <mrow> <mstyle displaystyle="true"> <msubsup> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <mrow> <mfenced> <mrow> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>−</mo> <msubsup> <mi>a</mi> <mi>i</mi> <mo>*</mo> </msubsup> </mrow> </mfenced> </mrow> </mstyle> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</div><div class='html-p'>(5) Support Vector Identification: After solving the dual problem, the Lagrange multipliers <span class='html-italic'>α<sub>i</sub></span> and <span class='html-italic'>α<sub>i</sub><sup>*</sup></span> are obtained. For data points x<span class='html-italic'><sub>i</sub></span> where <span class='html-italic'>α<sub>i</sub> </span>> 0 or <span class='html-italic'>α<sub>i</sub><sup>*</sup> </span>> 0, these points are considered support vectors, which play a decisive role in determining the position of the regression hyperplane.</div><div class='html-p'>(6) Decision Function: After identifying the support vectors, the final decision function can be written as follows (13):<div class='html-disp-formula-info' id='FD13-processes-12-02655'> <div class='f'> <math display='block'><semantics> <mrow> <mi>f</mi> <mfenced> <mi mathvariant="normal">x</mi> </mfenced> <mo>=</mo> <mstyle displaystyle="true"> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mfenced> <mrow> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>−</mo> <msubsup> <mi>α</mi> <mi>i</mi> <mo>*</mo> </msubsup> </mrow> </mfenced> <mi>K</mi> <mfenced> <mrow> <msub> <mi mathvariant="normal">x</mi> <mi>i</mi> </msub> <mo>,</mo> <mi mathvariant="normal">x</mi> </mrow> </mfenced> <mo>+</mo> <mi>b</mi> </mrow> </mstyle> </mrow> </semantics></math> </div> <div class='l'> <label >(13)</label> </div> </div> where <span class='html-italic'>b</span> is the bias term, which can be calculated using the support vectors.</div><div class='html-p'>(7) Regression Process: Use the obtained decision function <span class='html-italic'>f</span>(x) to predict the continuous target values for new input data, evaluating the regression results based on these predicted values.</div></section></section></section><section id='sec3-processes-12-02655' type=''><h2 data-nested='1'> 3. Data Preprocessing</h2><section id='sec3dot1-processes-12-02655' type=''><h4 class='html-italic' data-nested='2'> 3.1. Data Acquisition</h4><div class='html-p'>This study uses data from a coal mine’s comprehensive mining face, where gas over-limit situations frequently occur. To prevent major disasters such as gas explosions, this research focuses on predicting gas outburst quantities in the mining face. A total of 30 representative data samples containing 12 influencing factors were obtained from the monitoring data of the mine to serve as the original dataset, as shown in <a href="#processes-12-02655-t001" class="html-table">Table 1</a>.</div><div class='html-p'>In <a href="#processes-12-02655-t001" class="html-table">Table 1</a>, the 12 influencing factors are as follows: coal seam burial depth <span class='html-italic'>x</span><sub>1</sub> (m), coal seam gas content <span class='html-italic'>x</span><sub>2</sub> (m<sup>3</sup>/t), coal seam thickness <span class='html-italic'>x</span><sub>3</sub> (m), mining intensity <span class='html-italic'>x</span><sub>4</sub> (t/d), working face recovery rate <span class='html-italic'>x</span><sub>5</sub> (%), working face length <span class='html-italic'>x</span><sub>6</sub> (m), coal seam dip angle <span class='html-italic'>x</span><sub>7</sub> (°), adjacent layer gas content <span class='html-italic'>x</span><sub>8</sub> (m<sup>3</sup>/t), adjacent layer thickness <span class='html-italic'>x</span><sub>9</sub> (m), interlayer distance <span class='html-italic'>x</span><sub>10</sub> (m), mining height <span class='html-italic'>x</span><sub>11</sub> (m), and advance speed <span class='html-italic'>x</span><sub>12</sub> (m/d); the gas outburst quantity is represented as <span class='html-italic'>y</span> (m<sup>3</sup>/t). A total of 24 samples were randomly selected for the training set, while 6 samples were reserved for the testing set.</div></section><section id='sec3dot2-processes-12-02655' type=''><h4 class='html-italic' data-nested='2'> 3.2. Data Cleaning Based on Boxplot–MI</h4><div class='html-p'><a href="#processes-12-02655-t001" class="html-table">Table 1</a> presents the uncleaned data. MATLAB was used to clean the original dataset, beginning with the identification and handling of outliers using the Boxplot method. This involved calculating the lower and upper quartiles (Q1 and Q3) and the interquartile range (IQR) for each column of data, establishing upper and lower limits to identify which data points were outliers. These outliers were replaced with NaN to prevent them from affecting data analysis in subsequent processing. Next, multiple imputation (MI) was applied to fill in these missing values. In this study, six estimators were employed for imputing the missing values, including linear regression, logistic regression, decision trees (DTs), random forests (RFs), a support vector machine (SVM), and multilayer perceptrons (MLPs). The root mean square error (RMSE) was used to evaluate the imputation results and determine the best estimator. <a href="#processes-12-02655-f004" class="html-fig">Figure 4</a> illustrates the RMSE for each estimator. Observations from <a href="#processes-12-02655-f004" class="html-fig">Figure 4</a> indicate that the MLP imputation model, which achieved the lowest RMSE, demonstrates the highest accuracy. MLP neural networks excel in handling classification and regression problems, showing strong predictive performance and robustness. They are particularly well suited for complex datasets and high-dimensional data. Therefore, this study selected an MLP as the estimator for MI data imputation. The complete data are presented in <a href="#processes-12-02655-t002" class="html-table">Table 2</a> [<a href="#B27-processes-12-02655" class="html-bibr">27</a>,<a href="#B28-processes-12-02655" class="html-bibr">28</a>].</div></section><section id='sec3dot3-processes-12-02655' type=''><h4 class='html-italic' data-nested='2'> 3.3. Data Dimensionality Reduction Based on KPCA</h4><div class='html-p'>Kernel Principal Component Analysis (KPCA) utilizes kernel functions to map data into a high-dimensional feature space, effectively extracting underlying nonlinear structures and complex features. This characteristic significantly enhances the accuracy and efficiency of data analysis when dealing with high-dimensional and complex datasets. Furthermore, KPCA not only reduces dimensionality to improve the computational performance of models but also mitigates the impact of noise, thereby enhancing the expressive power of features.</div><div class='html-p'><a href="#processes-12-02655-f005" class="html-fig">Figure 5</a> shows the kernel matrix heatmap, which illustrates the similarity between data samples and reflects the structure of the kernel matrix calculated using a Gaussian kernel function. This heatmap provides a clearer analysis and identification of clustering trends and potential nonlinear relationships among the data samples. Each cell in the figure represents the similarity between two samples, with the color intensity indicating the level of similarity. Darker areas indicate high similarity, while lighter areas indicate low similarity. By observing <a href="#processes-12-02655-f005" class="html-fig">Figure 5</a>, clustering trends and potential nonlinear relationships between the samples can be visually identified. For instance, the similarity between the data in Group 1 and the data in Groups 2 and 3 is relatively high, as shown by the darker areas in the heatmap, indicating that these three groups exhibit similar patterns or behaviors in the feature space and are likely to belong to the same or nearby categories. In contrast, the similarity between the data in Group 1 and the data in Groups 10, 14, and 15 is low, as indicated by the lighter areas, suggesting significant differences between these samples and implying that they likely belong to different categories.</div><div class='html-p'>The variance explanation graph is shown in <a href="#processes-12-02655-f006" class="html-fig">Figure 6</a>, illustrating the proportion of total variance explained by each principal component. This graph serves as a tool for evaluating the importance and effectiveness of these components. The horizontal axis represents the component number, while the vertical axis shows the proportion of variance explained by each principal component. Typically, the first few principal components account for the majority of the variance, guiding the selection of an appropriate number of components to retain as much of the original data information as possible while reducing dimensionality and lowering computational complexity. Generally, a cumulative variance explanation ratio of 85% is considered a good balance between information retention and dimensionality reduction. In <a href="#processes-12-02655-f006" class="html-fig">Figure 6</a>, the cumulative variance explained by the first four principal components is calculated as 0.629978 + 0.116409 + 0.080876 + 0.062901 = 0.890164, which is greater than 0.85. Therefore, the first four principal components are selected for the reduced-dimensional data, with the reduced dataset presented in <a href="#processes-12-02655-t003" class="html-table">Table 3</a>.</div></section></section><section id='sec4-processes-12-02655' type=''><h2 data-nested='1'> 4. Establishment of Prediction Model</h2><section id='sec4dot1-processes-12-02655' type=''><h4 class='html-italic' data-nested='2'> 4.1. Optimization of Hyperparameters Based on the ICSA</h4><div class='html-p'><a href="#processes-12-02655-f007" class="html-fig">Figure 7</a> illustrates the optimization capabilities of the improved and original algorithms on unimodal and multimodal test functions. As shown, the fitness values of the ICSA convergence curves on all test functions improved after incorporating adaptive neighborhood search and reinforcement learning strategies. This indicates that these strategies effectively enhance the global optimization capability of the CSA.</div><div class='html-p'>In this study, three hyperparameters are optimized: Penalty Parameter <span class='html-italic'>C</span>: This parameter controls the model’s tolerance for error and determines the penalty for training errors. A higher <span class='html-italic'>C</span> value makes the model focus more on reducing training errors, potentially leading to overfitting. Conversely, a lower <span class='html-italic'>C</span> value yields a smoother model but may result in underfitting. Gaussian Kernel Bandwidth <span class='html-italic'>γ</span>: When using the RBF (Radial Basis Function) kernel, <span class='html-italic'>γ</span> controls the similarity measurement between samples and influences the model’s nonlinear mapping capability. A larger <span class='html-italic'>γ</span> value allows the model to capture finer details, increasing flexibility but risking overfitting. A smaller <span class='html-italic'>γ</span> value produces a smoother model with a higher risk of underfitting. Loss Function Parameter <span class='html-italic'>ϵ</span>: This parameter in the <span class='html-italic'>ϵ</span>-insensitive loss function defines the error tolerance range. A larger <span class='html-italic'>ϵ</span> value allows the model to ignore minor errors, reducing sensitivity to noise. A smaller <span class='html-italic'>ϵ</span> value improves model precision but may make it overly sensitive to noise.</div><div class='html-p'>After training, the optimal values for each parameter were obtained. The initialization range and optimal values of the ICSA parameter optimization are shown in <a href="#processes-12-02655-t004" class="html-table">Table 4</a>.</div></section><section id='sec4dot2-processes-12-02655' type=''><h4 class='html-italic' data-nested='2'> 4.2. Establishment of the KPCA-ICSA-SVR Prediction Model</h4><div class='html-p'>Substituting the optimal hyperparameter values obtained from the ICSA optimization into the SVR model, a gas emission prediction model based on KPCA-ICSA-SVR is established. The training set prediction results are shown in <a href="#processes-12-02655-f008" class="html-fig">Figure 8</a>. As observed from the figure, the RMSE of the training set prediction reaches 0.17898, with an R<sup>2</sup> of 0.9836, MAE of 0.1651, MSE of 0.032, and MAPE of 1.67%. All performance metrics are within reasonable ranges, indicating that the KPCA-ICSA-SVR model developed in this study for gas emission prediction is both reasonable and feasible.</div><div class='html-p'>The test set prediction results are shown in <a href="#processes-12-02655-f009" class="html-fig">Figure 9</a>. From the figure, it can be observed that the RMSE of the test set prediction reaches 0.3132, indicating that the model’s accuracy is within a reasonable range. This suggests that the KPCA-ICSA-SVR model does not exhibit overfitting or underfitting, demonstrating good generalization ability and enabling accurate predictions on new data.</div></section></section><section id='sec5-processes-12-02655' type=''><h2 data-nested='1'> 5. Evaluation and Comparison of Models</h2><section id='sec5dot1-processes-12-02655' type=''><h4 class='html-italic' data-nested='2'> 5.1. Test Set Performance Evaluation</h4><div class='html-p'>To validate the superiority of the KPCA-ICSA-SVR model established in this study, three comparative models were constructed: BP neural network [<a href="#B29-processes-12-02655" class="html-bibr">29</a>,<a href="#B30-processes-12-02655" class="html-bibr">30</a>,<a href="#B31-processes-12-02655" class="html-bibr">31</a>], KPCA-ICSA-BP, and SVR. Each model was applied to the test set for prediction, with the results presented in <a href="#processes-12-02655-t005" class="html-table">Table 5</a>. Due to the small dataset size, the computation time for all models is within 15 s. As shown in the table, the KPCA-ICSA-SVR model outperforms others across all evaluation metrics. Notably, the addition of KPCA for dimensionality reduction and the ICSA to the BP model significantly enhanced its predictive accuracy, indicating that the KPCA-ICSA method can effectively optimize prediction models.</div><div class='html-p'>(1) BP Model</div><div class='html-p'>The BP model performed moderately in predicting gas emissions, with an R<sup>2</sup> value indicating that approximately 85% of the data variance could be explained, suggesting a degree of underfitting. Both MAE and RMSE were relatively high, reflecting the model’s limitations in minimizing error, particularly in responding to larger errors (as RMSE slightly exceeded MAE). The MAPE value showed considerable variation across different data magnitudes, with a positive bias (MPE = 4.5%), indicating that BP predictions tended to overestimate actual values. This highlights the model’s lower sensitivity to small samples and extreme values. An MBE value of 0.4 confirmed a notable positive bias, indicating that the BP model tends to overestimate gas emissions.</div><div class='html-p'>Upon incorporating KPCA for feature extraction and the ICSA to optimize the BP model’s hyperparameters, the R<sup>2</sup> value improved significantly to 0.92, demonstrating that the model could explain 92% of data variance, with a considerable boost in fitting ability. Compared to the BP model, the KPCA-ICSA-BP model’s errors were notably reduced, reflecting that feature extraction and hyperparameter optimization successfully minimized predictive bias and improved stability. The model’s MAPE decreased by approximately 2.5%, enhancing prediction accuracy across various samples. A reduction in MPE indicated a better error distribution, and a lower MBE demonstrated decreased positive bias, confirming that KPCA and the ICSA effectively reduce systematic error.</div><div class='html-p'>(2) SVR Model</div><div class='html-p'>The SVR model outperformed the BP series in terms of fitting capability, achieving an R<sup>2</sup> value of 0.94, indicating SVR’s advantage in capturing the nonlinear characteristics of gas emission data. Both MAE and RMSE were better than those of BP and KPCA-ICSA-BP, showing that SVR effectively manages larger errors. Lower overall error highlighted SVR’s accuracy in predicting gas emissions, with a MAPE of 3.5%, reflecting strong stability in predictions. The negative MPE value suggested a slight tendency to underestimate gas emissions, though the error magnitude was small. The negative MBE value also confirmed a mild underestimation tendency, with minimal error.</div><div class='html-p'>The KPCA-ICSA-optimized SVR model achieved the highest R<sup>2</sup> value of 0.9752, demonstrating exceptional ability to explain the variance in gas emissions and superior fitting capability. Among the models, KPCA-ICSA-SVR had the lowest error rates, indicating robust control over both small and large errors. The MPE value was closer to zero, further affirming the model’s stability and precision in gas emission prediction. The near-zero MBE value suggested a very slight underestimation, but with minimal bias, making the model highly effective for prediction.</div></section><section id='sec5dot2-processes-12-02655' type=''><h4 class='html-italic' data-nested='2'> 5.2. Model Safety Adjustment</h4><div class='html-p'>Based on the model’s prediction results, a safety margin is added to the predicted gas emission values (14):<div class='html-disp-formula-info' id='FD14-processes-12-02655'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mover accent="true"> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mi>adjusted</mi> </mrow> </msub> <mo>=</mo> <mover accent="true"> <mi>y</mi> <mo>^</mo> </mover> <mo>+</mo> <msub> <mi>Δ</mi> <mrow> <mi>safety</mi> </mrow> </msub> </mrow> </semantics></math> </div> <div class='l'> <label >(14)</label> </div> </div> where Δ<sub>safety</sub> is a safety adjustment value set based on historical data and expert experience to ensure early warnings under high-risk conditions. The calculation formula is as follows (15):<div class='html-disp-formula-info' id='FD15-processes-12-02655'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>Δ</mi> <mrow> <mi>safety</mi> </mrow> </msub> <mo>=</mo> <mfenced close="|" open="|"> <mrow> <mi>MBE</mi> </mrow> </mfenced> <mo>+</mo> <mi>α</mi> </mrow> </semantics></math> </div> <div class='l'> <label >(15)</label> </div> </div> where <span class='html-italic'>α</span> is a compensation coefficient determined by the historical extreme values of gas emissions and the risk tolerance level. To ensure sufficient conservativeness, this study sets <span class='html-italic'>α</span> = 0.05, resulting in a Δ<sub>safety</sub> value of 0.165.</div><div class='html-p'>After incorporating the safety margin, the Mean Bias Error (MBE) in the model evaluation metrics reaches a positive value of 0.05, effectively improving the model’s safety.</div></section><section id='sec5dot3-processes-12-02655' type=''><h4 class='html-italic' data-nested='2'> 5.3. Model Generalization Verification</h4><div class='html-p'>To evaluate the applicability of the proposed model, 30 sets of field data from the reference [<a href="#B11-processes-12-02655" class="html-bibr">11</a>] were used for validation. In [<a href="#B11-processes-12-02655" class="html-bibr">11</a>], the test mine, located at the 12,322 main working face, has an average coal seam thickness of 6.25 m, including one to two layers of carbonaceous mudstone and mudstone interlayers. In areas affected by geological structures, the coal seam thickness varies significantly, with faults extending into the working face. These factors—variations in coal seam thickness, faulting, and interlayer disruptions—can cause periodic fluctuations in gas emission. Moreover, fault damage and stress concentration zones may lead to sudden large gas emissions, increasing the risk of unexpected outbursts. Therefore, accurate gas emission prediction is essential to ensure safe and orderly mining operations.</div><div class='html-p'>The sample data include 11 indicators, such as daily production of the working face, interlayer lithology, and coal seam thickness. The data samples were split into two groups; 80% were used for training and 20% for testing. The performance prediction results of different models are summarized in <a href="#processes-12-02655-t006" class="html-table">Table 6</a>.</div><div class='html-p'>As shown in the table, the KPCA-ICSA-SVR gas emission prediction model established in this study outperforms the models referenced in the literature across all evaluation metrics. This demonstrates that the proposed model has good applicability to other coal seams.</div></section></section><section id='sec6-processes-12-02655' type='discussion'><h2 data-nested='1'> 6. Discussion</h2><div class='html-p'>In summary, the gas emission prediction model based on KPCA-ICSA-SVR established in this study has high prediction accuracy. However, further discussions are needed in terms of data scale and other aspects.</div><div class='html-p'>Due to the constraints of the underground working environment, future research needs to incorporate more influencing factors for a comprehensive analysis. Gas emission is a complex, dynamic process influenced by multiple factors. Beyond the indicators considered in this study, additional potential factors, such as surrounding rock structure and the microscopic properties of coal, should be examined for a more thorough understanding and prediction of gas emission levels.</div><div class='html-p'>The mechanical properties and structural morphology of the surrounding rock, especially around the coal seam, significantly impact gas emissions. The strength, hardness, and fracture distribution of the surrounding rock determine the coal seam’s stability and permeability. Softer or more fractured surrounding rock provides pathways for gas to seep out, leading to increased gas emissions. Additionally, structural deformations within the surrounding rock, such as faults and folds, may cause localized pressure changes in the coal seam, further influencing gas release. Stable surrounding rock can effectively restrict gas diffusion, while unstable formations exacerbate gas emissions, thereby increasing safety risks in the mine.</div><div class='html-p'>The microscopic properties of coal, particularly its pore structure and gas adsorption characteristics, also play a crucial role in gas emissions. The porosity, pore distribution, and particle size of coal directly affect its gas storage capacity. Coal seams with well-developed pore structures can store more gas and release it rapidly under changing external conditions. Furthermore, areas with high gas adsorption capacity tend to absorb more gas molecules, which are then released at an accelerated rate during pressure changes. Other micro-level characteristics, such as coal type, composition, coalification degree, and moisture content, also significantly influence gas release behavior.</div><div class='html-p'>In conclusion, while the predictive model in this study has shown certain advantages, integrating more influencing indicators will further enhance the model’s accuracy and practicality, providing better decision support for gas emission prediction and disaster prevention.</div></section><section id='sec7-processes-12-02655' type='conclusions'><h2 data-nested='1'> 7. Conclusions</h2><div class='html-p'>This study conducts an in-depth analysis of data cleaning, feature extraction, and model optimization for gas emission prediction, proposing a high-precision prediction model based on KPCA-ICSA-SVR. Through data processing, dimensionality reduction, and algorithmic enhancements, this approach effectively captures the nonlinear relationships within complex data, significantly improving prediction accuracy and the model’s generalization capability. The application of this model provides essential technical support for mine gas management.</div><div class='html-p'>(1) Data Cleaning and Feature Extraction: In this study, the Boxplot–MI method was employed for comprehensive data cleaning of gas emission data. After removing outliers with the Boxplot method, multiple imputation (MI) was used to handle missing data, ensuring data completeness and consistency. Next, Kernel Principal Component Analysis (KPCA) was used to extract key features and perform effective dimensionality reduction. The first four principal components, which explain a cumulative variance of 0.89016, were selected. This approach not only significantly simplified the data structure but also effectively preserved the essential information between variables.</div><div class='html-p'>(2) Model Optimization: An Improved Crow Search Algorithm (ICSA) was developed, integrating adaptive neighborhood search with reinforcement learning to optimize the SVR model’s hyperparameters. By adaptively adjusting the neighborhood range and employing reinforcement learning strategies for dynamic exploration of the global optimum, the ICSA efficiently and stably identified the optimal parameter combination for SVR, enhancing model convergence speed and accuracy.</div><div class='html-p'>(3) Comparative Experiment: A series of comparative experiments, including BP, KPCA-ICSA-BP, and conventional SVR models, were conducted to assess each model’s performance in gas emission prediction. Results demonstrated that the RMSE of the KPCA-ICSA-SVR model for the test set is 0.3132, which is lower than that of other models. Additionally, all other evaluation metrics show optimal performance, particularly in terms of prediction accuracy and generalization ability, surpassing the performance of other models.</div></section> </div> <div class="html-back"> <section class='html-notes'><h2 >Author Contributions</h2><div class='html-p'>Conceptualization, L.L.; methodology, L.L. and X.M.; software, L.D.; validation, Y.C. and Y.J.; formal analysis, L.D. and X.M.; investigation, Y.J.; writing—original draft preparation, L.L. and L.D. All authors have read and agreed to the published version of the manuscript.</div></section><section class='html-notes'><h2>Funding</h2><div class='html-p'>This research was funded by the Natural Science Foundation of Chongqing, grant number CSTB2022NSCQ-MSX1080; the Key Project of Science and Technology Innovation and Entrepreneurship Fund of Tiandi Technology Co., Ltd., grant number 2023-2-TD-ZD001; and the Science and Technology Project of Yulin, grant number CXY-2020-030.</div></section><section class='html-notes'><h2 >Data Availability Statement</h2><div class='html-p'>The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding authors. </div></section><section class='html-notes'><h2 >Conflicts of Interest</h2><div class='html-p'>The authors declare that this study received funding from the Key Project of Science and Technology Innovation and Entrepreneurship Fund of Tiandi Technology Co., Ltd. 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data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g001.png" alt="Processes 12 02655 g001" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g001-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f001"></a> </div> </div> <div class="html-fig_description"> <b>Figure 1.</b> Schematic diagram of KPCA.  </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02655-f001"> <div class="html-caption"> <b>Figure 1.</b> Schematic diagram of KPCA.</div> <div class="html-img"><img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g001.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g001.png" alt="Processes 12 02655 g001" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g001.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02655-f002"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f002"> <img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g002.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g002.png" alt="Processes 12 02655 g002" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g002-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f002"></a> </div> </div> <div class="html-fig_description"> <b>Figure 2.</b> Schematic diagram of the ICSA.  </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02655-f002"> <div class="html-caption"> <b>Figure 2.</b> Schematic diagram of the ICSA.</div> <div class="html-img"><img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g002.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g002.png" alt="Processes 12 02655 g002" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g002.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02655-f003"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f003"> <img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g003.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g003.png" alt="Processes 12 02655 g003" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g003-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f003"></a> </div> </div> <div class="html-fig_description"> <b>Figure 3.</b> Schematic diagram of SVR.  </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02655-f003"> <div class="html-caption"> <b>Figure 3.</b> Schematic diagram of SVR.</div> <div class="html-img"><img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g003.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g003.png" alt="Processes 12 02655 g003" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g003.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02655-f004"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f004"> <img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g004.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g004.png" alt="Processes 12 02655 g004" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g004-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f004"></a> </div> </div> <div class="html-fig_description"> <b>Figure 4.</b> RMSE of different estimators.  </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02655-f004"> <div class="html-caption"> <b>Figure 4.</b> RMSE of different estimators.</div> <div class="html-img"><img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g004.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g004.png" alt="Processes 12 02655 g004" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g004.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02655-f005"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f005"> <img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g005.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g005.png" alt="Processes 12 02655 g005" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g005-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f005"></a> </div> </div> <div class="html-fig_description"> <b>Figure 5.</b> Kernel matrix heatmap.  </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02655-f005"> <div class="html-caption"> <b>Figure 5.</b> Kernel matrix heatmap.</div> <div class="html-img"><img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g005.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g005.png" alt="Processes 12 02655 g005" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g005.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02655-f006"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f006"> <img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g006.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g006.png" alt="Processes 12 02655 g006" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g006-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f006"></a> </div> </div> <div class="html-fig_description"> <b>Figure 6.</b> Variance explanation.  </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02655-f006"> <div class="html-caption"> <b>Figure 6.</b> Variance explanation.</div> <div class="html-img"><img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g006.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g006.png" alt="Processes 12 02655 g006" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g006.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02655-f007"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f007"> <img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g007.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g007.png" alt="Processes 12 02655 g007" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g007-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f007"></a> </div> </div> <div class="html-fig_description"> <b>Figure 7.</b> Optimization capabilities of the algorithm: (<b>a</b>) unimodal function; (<b>b</b>) multimodal function.  </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02655-f007"> <div class="html-caption"> <b>Figure 7.</b> Optimization capabilities of the algorithm: (<b>a</b>) unimodal function; (<b>b</b>) multimodal function.</div> <div class="html-img"><img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g007.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g007.png" alt="Processes 12 02655 g007" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g007.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02655-f008"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f008"> <img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g008.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g008.png" alt="Processes 12 02655 g008" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g008-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f008"></a> </div> </div> <div class="html-fig_description"> <b>Figure 8.</b> Training set prediction results.  </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02655-f008"> <div class="html-caption"> <b>Figure 8.</b> Training set prediction results.</div> <div class="html-img"><img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g008.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g008.png" alt="Processes 12 02655 g008" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g008.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02655-f009"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f009"> <img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g009.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g009.png" alt="Processes 12 02655 g009" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g009-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#fig_body_display_processes-12-02655-f009"></a> </div> </div> <div class="html-fig_description"> <b>Figure 9.</b> Test set prediction results  </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02655-f009"> <div class="html-caption"> <b>Figure 9.</b> Test set prediction results</div> <div class="html-img"><img data-large="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g009.png" data-original="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g009.png" alt="Processes 12 02655 g009" data-lsrc="/processes/processes-12-02655/article_deploy/html/images/processes-12-02655-g009.png" /></div> </div> <div class="html-table-wrap" id="processes-12-02655-t001"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href='#table_body_display_processes-12-02655-t001'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#table_body_display_processes-12-02655-t001"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 1.</b> Partial raw data. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02655-t001"> <div class="html-caption"><b>Table 1.</b> Partial raw data.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' > </th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>1</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>2</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>3</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>4</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>5</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>6</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>7</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>8</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>9</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>10</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>11</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>12</sub></th><th align='center' valign='top' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>y</span></th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >1</td><td align='center' valign='top' class='html-align-center' >408</td><td align='center' valign='top' class='html-align-center' >2.04</td><td align='center' valign='top' class='html-align-center' >2.4</td><td align='center' valign='top' class='html-align-center' >1839</td><td align='center' valign='top' class='html-align-center' >0.95</td><td align='center' valign='top' class='html-align-center' >163</td><td align='center' valign='top' class='html-align-center' >11</td><td align='center' valign='top' class='html-align-center' >2.34</td><td align='center' valign='top' class='html-align-center' >1.5</td><td align='center' valign='top' class='html-align-center' >20</td><td align='center' valign='top' class='html-align-center' >2.4</td><td align='center' valign='top' class='html-align-center' >4.6</td><td align='center' valign='top' class='html-align-center' >3.54</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >2</td><td align='center' valign='top' class='html-align-center' >415</td><td align='center' valign='top' class='html-align-center' >2.46</td><td align='center' valign='top' class='html-align-center' >20.3</td><td align='center' valign='top' class='html-align-center' >1639</td><td align='center' valign='top' class='html-align-center' >0.96</td><td align='center' valign='top' class='html-align-center' >158</td><td align='center' valign='top' class='html-align-center' >11</td><td align='center' valign='top' class='html-align-center' >2.42</td><td align='center' valign='top' class='html-align-center' >1.23</td><td align='center' valign='top' class='html-align-center' >21</td><td align='center' valign='top' class='html-align-center' >2.3</td><td align='center' valign='top' class='html-align-center' >4.54</td><td align='center' valign='top' class='html-align-center' >4.07</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >3</td><td align='center' valign='top' class='html-align-center' >430</td><td align='center' valign='top' class='html-align-center' >2.4</td><td align='center' valign='top' class='html-align-center' >2.1</td><td align='center' valign='top' class='html-align-center' >1770</td><td align='center' valign='top' class='html-align-center' >0.96</td><td align='center' valign='top' class='html-align-center' > </td><td align='center' valign='top' class='html-align-center' >12</td><td align='center' valign='top' class='html-align-center' >2.35</td><td align='center' valign='top' class='html-align-center' >1.48</td><td align='center' valign='top' class='html-align-center' >23</td><td align='center' valign='top' class='html-align-center' >2.1</td><td align='center' valign='top' class='html-align-center' >4</td><td align='center' valign='top' class='html-align-center' >4.17</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='top' class='html-align-center' >439</td><td align='center' valign='top' class='html-align-center' >2.79</td><td align='center' valign='top' class='html-align-center' >2.6</td><td align='center' valign='top' class='html-align-center' >2091</td><td align='center' valign='top' class='html-align-center' >0.95</td><td align='center' valign='top' class='html-align-center' >149</td><td align='center' valign='top' class='html-align-center' >12</td><td align='center' valign='top' class='html-align-center' >2.45</td><td align='center' valign='top' class='html-align-center' >1.81</td><td align='center' valign='top' class='html-align-center' >19</td><td align='center' valign='top' class='html-align-center' >2.6</td><td align='center' valign='top' class='html-align-center' >4.76</td><td align='center' valign='top' class='html-align-center' >4.56</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >5</td><td align='center' valign='top' class='html-align-center' >460</td><td align='center' valign='top' class='html-align-center' >2.71</td><td align='center' valign='top' class='html-align-center' >2.6</td><td align='center' valign='top' class='html-align-center' >2120</td><td align='center' valign='top' class='html-align-center' >0.95</td><td align='center' valign='top' class='html-align-center' >165</td><td align='center' valign='top' class='html-align-center' >16</td><td align='center' valign='top' class='html-align-center' >2.31</td><td align='center' valign='top' class='html-align-center' >1.7</td><td align='center' valign='top' class='html-align-center' >109</td><td align='center' valign='top' class='html-align-center' >2.6</td><td align='center' valign='top' class='html-align-center' >4.59</td><td align='center' valign='top' class='html-align-center' >4.3</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >6</td><td align='center' valign='top' class='html-align-center' >541</td><td align='center' valign='top' class='html-align-center' >3.6</td><td align='center' valign='top' class='html-align-center' >3.1</td><td align='center' valign='top' class='html-align-center' > </td><td align='center' valign='top' class='html-align-center' >0.95</td><td align='center' valign='top' class='html-align-center' >180</td><td align='center' valign='top' class='html-align-center' >12</td><td align='center' valign='top' class='html-align-center' >3.05</td><td align='center' valign='top' class='html-align-center' >1.6</td><td align='center' valign='top' class='html-align-center' >19</td><td align='center' valign='top' class='html-align-center' >3.1</td><td align='center' valign='top' class='html-align-center' >4</td><td align='center' valign='top' class='html-align-center' >5.07</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >7</td><td align='center' valign='top' class='html-align-center' >545</td><td align='center' valign='top' class='html-align-center' >3.25</td><td align='center' valign='top' class='html-align-center' >3.3</td><td align='center' valign='top' class='html-align-center' >2006</td><td align='center' valign='top' class='html-align-center' >0.95</td><td align='center' valign='top' class='html-align-center' >168</td><td align='center' valign='top' class='html-align-center' >13</td><td align='center' valign='top' class='html-align-center' >2.46</td><td align='center' valign='top' class='html-align-center' >1.6</td><td align='center' valign='top' class='html-align-center' >20</td><td align='center' valign='top' class='html-align-center' >3.3</td><td align='center' valign='top' class='html-align-center' >3.93</td><td align='center' valign='top' class='html-align-center' >4.64</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >8</td><td align='center' valign='top' class='html-align-center' >608</td><td align='center' valign='top' class='html-align-center' >4.04</td><td align='center' valign='top' class='html-align-center' >3.55</td><td align='center' valign='top' class='html-align-center' >2586</td><td align='center' valign='top' class='html-align-center' >0.91</td><td align='center' valign='top' class='html-align-center' >170</td><td align='center' valign='top' class='html-align-center' >11</td><td align='center' valign='top' class='html-align-center' >3.18</td><td align='center' valign='top' class='html-align-center' >1.72</td><td align='center' valign='top' class='html-align-center' >21</td><td align='center' valign='top' class='html-align-center' >3.4</td><td align='center' valign='top' class='html-align-center' >4.18</td><td align='center' valign='top' class='html-align-center' >6.16</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >9</td><td align='center' valign='middle' class='html-align-center' >615</td><td align='center' valign='middle' class='html-align-center' >4.92</td><td align='center' valign='middle' class='html-align-center' >6.3</td><td align='center' valign='middle' class='html-align-center' >3395</td><td align='center' valign='middle' class='html-align-center' >0.802</td><td align='center' valign='middle' class='html-align-center' >172</td><td align='center' valign='middle' class='html-align-center' >12</td><td align='center' valign='middle' class='html-align-center' >3.3</td><td align='center' valign='middle' class='html-align-center' >1.6</td><td align='center' valign='middle' class='html-align-center' >14</td><td align='center' valign='middle' class='html-align-center' >6.3</td><td align='center' valign='middle' class='html-align-center' >3.39</td><td align='center' valign='middle' class='html-align-center' >7.58</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >…</td><td align='center' valign='top' class='html-align-center' >…</td><td align='center' valign='top' class='html-align-center' >…</td><td align='center' valign='top' class='html-align-center' >…</td><td align='center' valign='top' class='html-align-center' >…</td><td align='center' valign='top' class='html-align-center' >…</td><td align='center' valign='top' class='html-align-center' >…</td><td align='center' valign='top' class='html-align-center' >…</td><td align='center' valign='top' class='html-align-center' >…</td><td align='center' valign='top' class='html-align-center' >…</td><td align='center' valign='top' class='html-align-center' >…</td><td align='center' valign='top' class='html-align-center' >…</td><td align='center' valign='top' class='html-align-center' >…</td><td align='center' valign='top' class='html-align-center' > </td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >30</td><td align='center' valign='top' style='border-bottom:solid thin' class='html-align-center' >611</td><td align='center' valign='top' style='border-bottom:solid thin' class='html-align-center' >4.05</td><td align='center' valign='top' style='border-bottom:solid thin' class='html-align-center' >6.7</td><td align='center' valign='top' style='border-bottom:solid thin' class='html-align-center' >3354</td><td align='center' valign='top' style='border-bottom:solid thin' class='html-align-center' >0.812</td><td align='center' valign='top' style='border-bottom:solid thin' class='html-align-center' >175</td><td align='center' valign='top' style='border-bottom:solid thin' class='html-align-center' >9</td><td align='center' valign='top' style='border-bottom:solid thin' class='html-align-center' >3.15</td><td align='center' valign='top' style='border-bottom:solid thin' class='html-align-center' >1.8</td><td align='center' valign='top' style='border-bottom:solid thin' class='html-align-center' >16</td><td align='center' valign='top' style='border-bottom:solid thin' class='html-align-center' >6.7</td><td align='center' valign='top' style='border-bottom:solid thin' class='html-align-center' >2.64</td><td align='center' valign='top' style='border-bottom:solid thin' class='html-align-center' >7.8</td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02655-t002"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href='#table_body_display_processes-12-02655-t002'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#table_body_display_processes-12-02655-t002"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 2.</b> Partial complete data. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02655-t002"> <div class="html-caption"><b>Table 2.</b> Partial complete data.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' > </th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>1</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>2</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>3</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>4</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>5</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>6</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>7</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>8</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>9</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>10</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>11</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>x</span><sub>12</sub></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>y</span></th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >1</td><td align='center' valign='middle' class='html-align-center' >408</td><td align='center' valign='middle' class='html-align-center' >2.04</td><td align='center' valign='middle' class='html-align-center' >2.4</td><td align='center' valign='middle' class='html-align-center' >1839</td><td align='center' valign='middle' class='html-align-center' >0.95</td><td align='center' valign='middle' class='html-align-center' >163</td><td align='center' valign='middle' class='html-align-center' >11</td><td align='center' valign='middle' class='html-align-center' >2.34</td><td align='center' valign='middle' class='html-align-center' >1.5</td><td align='center' valign='middle' class='html-align-center' >20</td><td align='center' valign='middle' class='html-align-center' >2.4</td><td align='center' valign='middle' class='html-align-center' >4.6</td><td align='center' valign='middle' class='html-align-center' >3.54</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >2</td><td align='center' valign='middle' class='html-align-center' >415</td><td align='center' valign='middle' class='html-align-center' >2.46</td><td align='center' valign='middle' class='html-align-center' >2.3</td><td align='center' valign='middle' class='html-align-center' >1639</td><td align='center' valign='middle' class='html-align-center' >0.96</td><td align='center' valign='middle' class='html-align-center' >158</td><td align='center' valign='middle' class='html-align-center' >11</td><td align='center' valign='middle' class='html-align-center' >2.42</td><td align='center' valign='middle' class='html-align-center' >1.23</td><td align='center' valign='middle' class='html-align-center' >21</td><td align='center' valign='middle' class='html-align-center' >2.3</td><td align='center' valign='middle' class='html-align-center' >4.54</td><td align='center' valign='middle' class='html-align-center' >4.07</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >3</td><td align='center' valign='middle' class='html-align-center' >430</td><td align='center' valign='middle' class='html-align-center' >2.4</td><td align='center' valign='middle' class='html-align-center' >2.1</td><td align='center' valign='middle' class='html-align-center' >1770</td><td align='center' valign='middle' class='html-align-center' >0.96</td><td align='center' valign='middle' class='html-align-center' >176</td><td align='center' valign='middle' class='html-align-center' >12</td><td align='center' valign='middle' class='html-align-center' >2.35</td><td align='center' valign='middle' class='html-align-center' >1.48</td><td align='center' valign='middle' class='html-align-center' >23</td><td align='center' valign='middle' class='html-align-center' >2.1</td><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' >4.17</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' >439</td><td align='center' valign='middle' class='html-align-center' >2.79</td><td align='center' valign='middle' class='html-align-center' >2.6</td><td align='center' valign='middle' class='html-align-center' >2091</td><td align='center' valign='middle' class='html-align-center' >0.95</td><td align='center' valign='middle' class='html-align-center' >149</td><td align='center' valign='middle' class='html-align-center' >12</td><td align='center' valign='middle' class='html-align-center' >2.45</td><td align='center' valign='middle' class='html-align-center' >1.81</td><td align='center' valign='middle' class='html-align-center' >19</td><td align='center' valign='middle' class='html-align-center' >2.6</td><td align='center' valign='middle' class='html-align-center' >4.76</td><td align='center' valign='middle' class='html-align-center' >4.56</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >5</td><td align='center' valign='middle' class='html-align-center' >460</td><td align='center' valign='middle' class='html-align-center' >2.71</td><td align='center' valign='middle' class='html-align-center' >2.6</td><td align='center' valign='middle' class='html-align-center' >2120</td><td align='center' valign='middle' class='html-align-center' >0.95</td><td align='center' valign='middle' class='html-align-center' >165</td><td align='center' valign='middle' class='html-align-center' >16</td><td align='center' valign='middle' class='html-align-center' >2.31</td><td align='center' valign='middle' class='html-align-center' >1.7</td><td align='center' valign='middle' class='html-align-center' >19</td><td align='center' valign='middle' class='html-align-center' >2.6</td><td align='center' valign='middle' class='html-align-center' >4.59</td><td align='center' valign='middle' class='html-align-center' >4.3</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >6</td><td align='center' valign='middle' class='html-align-center' >541</td><td align='center' valign='middle' class='html-align-center' >3.6</td><td align='center' valign='middle' class='html-align-center' >3.1</td><td align='center' valign='middle' class='html-align-center' >2250</td><td align='center' valign='middle' class='html-align-center' >0.95</td><td align='center' valign='middle' class='html-align-center' >180</td><td align='center' valign='middle' class='html-align-center' >12</td><td align='center' valign='middle' class='html-align-center' >3.05</td><td align='center' valign='middle' class='html-align-center' >1.6</td><td align='center' valign='middle' class='html-align-center' >19</td><td align='center' valign='middle' class='html-align-center' >3.1</td><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' >5.07</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >7</td><td align='center' valign='middle' class='html-align-center' >545</td><td align='center' valign='middle' class='html-align-center' >3.25</td><td align='center' valign='middle' class='html-align-center' >3.3</td><td align='center' valign='middle' class='html-align-center' >2006</td><td align='center' valign='middle' class='html-align-center' >0.95</td><td align='center' valign='middle' class='html-align-center' >168</td><td align='center' valign='middle' class='html-align-center' >13</td><td align='center' valign='middle' class='html-align-center' >2.46</td><td align='center' valign='middle' class='html-align-center' >1.6</td><td align='center' valign='middle' class='html-align-center' >20</td><td align='center' valign='middle' class='html-align-center' >3.3</td><td align='center' valign='middle' class='html-align-center' >3.93</td><td align='center' valign='middle' class='html-align-center' >4.64</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >8</td><td align='center' valign='middle' class='html-align-center' >608</td><td align='center' valign='middle' class='html-align-center' >4.04</td><td align='center' valign='middle' class='html-align-center' >3.55</td><td align='center' valign='middle' class='html-align-center' >2586</td><td align='center' valign='middle' class='html-align-center' >0.91</td><td align='center' valign='middle' class='html-align-center' >170</td><td align='center' valign='middle' class='html-align-center' >11</td><td align='center' valign='middle' class='html-align-center' >3.18</td><td align='center' valign='middle' class='html-align-center' >1.72</td><td align='center' valign='middle' class='html-align-center' >21</td><td align='center' valign='middle' class='html-align-center' >3.4</td><td align='center' valign='middle' class='html-align-center' >4.18</td><td align='center' valign='middle' class='html-align-center' >6.16</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >9</td><td align='center' valign='middle' class='html-align-center' >615</td><td align='center' valign='middle' class='html-align-center' >4.92</td><td align='center' valign='middle' class='html-align-center' >6.3</td><td align='center' valign='middle' class='html-align-center' >3395</td><td align='center' valign='middle' class='html-align-center' >0.802</td><td align='center' valign='middle' class='html-align-center' >172</td><td align='center' valign='middle' class='html-align-center' >12</td><td align='center' valign='middle' class='html-align-center' >3.3</td><td align='center' valign='middle' class='html-align-center' >1.6</td><td align='center' valign='middle' class='html-align-center' >14</td><td align='center' valign='middle' class='html-align-center' >6.3</td><td align='center' valign='middle' class='html-align-center' >3.39</td><td align='center' valign='middle' class='html-align-center' >7.58</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >…</td><td align='center' valign='middle' class='html-align-center' >…</td><td align='center' valign='middle' class='html-align-center' >…</td><td align='center' valign='middle' class='html-align-center' >…</td><td align='center' valign='middle' class='html-align-center' >…</td><td align='center' valign='middle' class='html-align-center' >…</td><td align='center' valign='middle' class='html-align-center' >…</td><td align='center' valign='middle' class='html-align-center' >…</td><td align='center' valign='middle' class='html-align-center' >…</td><td align='center' valign='middle' class='html-align-center' >…</td><td align='center' valign='middle' class='html-align-center' >…</td><td align='center' valign='middle' class='html-align-center' >…</td><td align='center' valign='middle' class='html-align-center' >…</td><td align='center' valign='middle' class='html-align-center' >…</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >30</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >611</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.05</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.7</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3354</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.812</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >175</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.15</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.8</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >16</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.7</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.64</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.8</td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02655-t003"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href='#table_body_display_processes-12-02655-t003'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#table_body_display_processes-12-02655-t003"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 3.</b> Partial data after dimensionality reduction. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02655-t003"> <div class="html-caption"><b>Table 3.</b> Partial data after dimensionality reduction.</div> <table > <thead ><tr ><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' > </th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >P1</th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >P2</th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >P3</th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >P4</th></tr></thead><tbody ><tr ><td align='left' valign='middle' class='html-align-left' >1</td><td align='left' valign='middle' class='html-align-left' >−0.070030966</td><td align='left' valign='middle' class='html-align-left' >−0.007384908</td><td align='left' valign='middle' class='html-align-left' >0.001259093</td><td align='left' valign='middle' class='html-align-left' >−0.003374653</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >2</td><td align='left' valign='middle' class='html-align-left' >−0.075670036</td><td align='left' valign='middle' class='html-align-left' >−0.019152051</td><td align='left' valign='middle' class='html-align-left' >0.005231675</td><td align='left' valign='middle' class='html-align-left' >−0.007859444</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >3</td><td align='left' valign='middle' class='html-align-left' >−0.061941622</td><td align='left' valign='middle' class='html-align-left' >−0.001682007</td><td align='left' valign='middle' class='html-align-left' >0.003784321</td><td align='left' valign='middle' class='html-align-left' >−0.01279089</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >4</td><td align='left' valign='middle' class='html-align-left' >−0.057579009</td><td align='left' valign='middle' class='html-align-left' >0.005133138</td><td align='left' valign='middle' class='html-align-left' >−0.010676203</td><td align='left' valign='middle' class='html-align-left' >0.007044164</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >5</td><td align='left' valign='middle' class='html-align-left' >−0.0542516</td><td align='left' valign='middle' class='html-align-left' >0.018470685</td><td align='left' valign='middle' class='html-align-left' >−0.000564319</td><td align='left' valign='middle' class='html-align-left' >−0.002088861</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >6</td><td align='left' valign='middle' class='html-align-left' >−0.00737452</td><td align='left' valign='middle' class='html-align-left' >0.004864428</td><td align='left' valign='middle' class='html-align-left' >0.005790376</td><td align='left' valign='middle' class='html-align-left' >−0.010555114</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >7</td><td align='left' valign='middle' class='html-align-left' >−0.026565961</td><td align='left' valign='middle' class='html-align-left' >0.005300026</td><td align='left' valign='middle' class='html-align-left' >0.000784251</td><td align='left' valign='middle' class='html-align-left' >−0.004548474</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >8</td><td align='left' valign='middle' class='html-align-left' >0.009923864</td><td align='left' valign='middle' class='html-align-left' >0.002950055</td><td align='left' valign='middle' class='html-align-left' >−0.005103689</td><td align='left' valign='middle' class='html-align-left' >−0.00680728</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >9</td><td align='left' valign='middle' class='html-align-left' >0.080811222</td><td align='left' valign='middle' class='html-align-left' >−0.00030095</td><td align='left' valign='middle' class='html-align-left' >0.002270081</td><td align='left' valign='middle' class='html-align-left' >−0.001053749</td></tr><tr ><td align='left' valign='middle' class='html-align-left' >…</td><td align='left' valign='middle' class='html-align-left' >…</td><td align='left' valign='middle' class='html-align-left' >…</td><td align='left' valign='middle' class='html-align-left' >…</td><td align='left' valign='middle' class='html-align-left' >…</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >30</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.085891336</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.002544488</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.005689592</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.001248051</td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02655-t004"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href='#table_body_display_processes-12-02655-t004'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#table_body_display_processes-12-02655-t004"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 4.</b> ICSA optimization parameters’ initial range and optimal value. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02655-t004"> <div class="html-caption"><b>Table 4.</b> ICSA optimization parameters’ initial range and optimal value.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Number</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Hyperparameter</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Initialization Scope</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Optimal Configuration</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >1</td><td align='center' valign='middle' class='html-align-center' ><span class='html-italic'>C</span></td><td align='center' valign='middle' class='html-align-center' >0.1~1000</td><td align='center' valign='middle' class='html-align-center' >1.0587</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >2</td><td align='center' valign='middle' class='html-align-center' ><span class='html-italic'>γ</span></td><td align='center' valign='middle' class='html-align-center' >10<sup>−6</sup>~10</td><td align='center' valign='middle' class='html-align-center' >0.0063</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>ϵ</span></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.001~1</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.1</td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02655-t005"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href='#table_body_display_processes-12-02655-t005'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#table_body_display_processes-12-02655-t005"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 5.</b> Comparison of model prediction results. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02655-t005"> <div class="html-caption"><b>Table 5.</b> Comparison of model prediction results.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Model</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >R<sup>2</sup></th><th align='center' valign='top' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >MAE</th><th align='center' valign='top' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >MAPE/%</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >MBE</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RMSE</th><th align='center' valign='top' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >MPE/%</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >BP</td><td align='center' valign='middle' class='html-align-center' >0.8564</td><td align='center' valign='middle' class='html-align-center' >0.5017</td><td align='center' valign='middle' class='html-align-center' >6.56</td><td align='center' valign='middle' class='html-align-center' >0.4011</td><td align='center' valign='middle' class='html-align-center' >0.6041</td><td align='center' valign='top' class='html-align-center' >4.51</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >KPCA-ICSA-BP</td><td align='center' valign='middle' class='html-align-center' >0.9252</td><td align='center' valign='middle' class='html-align-center' >0.3524</td><td align='center' valign='middle' class='html-align-center' >4.14</td><td align='center' valign='middle' class='html-align-center' >0.2519</td><td align='center' valign='middle' class='html-align-center' >0.4786</td><td align='center' valign='top' class='html-align-center' >3.09</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SVR</td><td align='center' valign='middle' class='html-align-center' >0.9436</td><td align='center' valign='middle' class='html-align-center' >0.2879</td><td align='center' valign='middle' class='html-align-center' >3.50</td><td align='center' valign='middle' class='html-align-center' >−0.1577</td><td align='center' valign='middle' class='html-align-center' >0.3568</td><td align='center' valign='top' class='html-align-center' >−2.07</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >KPCA-ICSA-SVR</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.9752</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.2108</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.01</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−0.1150</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.3071</td><td align='center' valign='top' style='border-bottom:solid thin' class='html-align-center' >−1.74</td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02655-t006"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href='#table_body_display_processes-12-02655-t006'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/12/2655/display" href="#table_body_display_processes-12-02655-t006"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 6.</b> Performance comparison. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02655-t006"> <div class="html-caption"><b>Table 6.</b> Performance comparison.</div> <table > <thead ><tr ><th colspan='2' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Model</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Maximum Error %</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Minimum Error %</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Average Error %</th></tr></thead><tbody ><tr ><td rowspan='3' align='center' valign='middle' class='html-align-center' >Reference [<a href="#B11-processes-12-02655" class="html-bibr">11</a>]</td><td align='center' valign='middle' class='html-align-center' >RBF</td><td align='center' valign='middle' class='html-align-center' >16.29</td><td align='center' valign='middle' class='html-align-center' >0.77</td><td align='center' valign='middle' class='html-align-center' >7.28</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >FA-PSO-RBF</td><td align='center' valign='middle' class='html-align-center' >11.64</td><td align='center' valign='middle' class='html-align-center' >0.25</td><td align='center' valign='middle' class='html-align-center' >5.65</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >FA-AQPSO-RBF</td><td align='center' valign='middle' class='html-align-center' >9.27</td><td align='center' valign='middle' class='html-align-center' >0.22</td><td align='center' valign='middle' class='html-align-center' >2.59</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >This model</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >KPCA-ICSA-SVR</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.01</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.12</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.37</td></tr></tbody> </table> </div> </section><section class='html-fn_group'><table><tr id=''><td></td><td><div class='html-p'><b>Disclaimer/Publisher’s Note:</b> The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). 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